Relativistic Timing

1. The problem statement, all variables and given/known data
A member of a colony on Jupiter is required to salute the UN flag at the same time as it is being done on Earth at noon in New York. If observers in all inertial frames(i.e. any observer traveling at any arbitrary velocity) are to agree that he has performed his duty, how long must he solute for(i.e. seeing you don't know how fast the observer is traveling, what time iterval ensures that the rising of the falg and the saluting are simultaneous for all possible speeds of the observer)? (Distance between the planets is approximately 8 x10^6 km, ignore any relative motion of the planets)

2. Relevant equations

Lorentz Transformation

3. The attempt at a solution

I need help getting started on this. I have no idea what to do at all(partly because of not understanding what the question wants) I'm not sure if I'm suppose to derive an equation, or there is a number answer to this.

I'm totally stuck on the thought process portion and cannot/don't know how to translate anything onto paper.
I know that the arbitrary observer can have velocity from the range of -c to c but I don't know if that means I should end up with two solutions which will give us the time interval.

So any advice on how to begin this would be greatly appreciated. Thanks

This is a straightforward application of the lorentz transformation for time. You know that time slows down due to relative motion and it takes some time for light to travel some distance, so for the special case that the relative velocity of Jupiter and Earth are 0, the amount of time should be (Distance from Earth to Jupiter)/c.

There will be an infinite number of solutions (one that corresponds to each of the possible relative velocities that the planets could be moving with).

This is a straightforward application of the lorentz transformation for time. You know that time slows down due to relative motion and it takes some time for light to travel some distance, so for the special case that the relative velocity of Jupiter and Earth are 0, the amount of time should be (Distance from Earth to Jupiter)/c.

There will be an infinite number of solutions (one that corresponds to each of the possible relative velocities that the planets could be moving with).

Are you saying all I have to do is to apply time dilation factor to (Distance from Earth to Jupiter)/c?

There is only one way that all inertial observers will agree that they are simultaneous. He has to hold the salute for a time that includes all spacelike intervals from noon in NY on Earth to Jupiter. Draw a light cone.

There is only one way that all inertial observers will agree that they are simultaneous. He has to hold the salute for a time that includes all spacelike intervals from noon in NY on Earth to Jupiter. Draw a light cone.

This is still not making sense to me. I understand that the person on Jupiter has to hold the salute for the time it takes to travel between the planets. But what does a light cone have anything to do with this?

The person has to be holding it in the past of the event as well as in the future of the event until all inertial observers agree they are simultaneous. The only events that can be considered as simultaneous are outside of the mutual light cones of either event.